I'm not sure what you are trying to state. What do you think is a moral dilemma? If acting against the character's defined nature as a result of a moral dilemma isn't a moral dilemma then neither is acting with the character's defined nature. The only alternative to that would be trinary logic with no defined nature, but in practice what I find from no defined nature is that there definitely then is no moral dilemma as the nature will be defined at the moment as what is convenient and then redefined conveniently at the next test. At least if there is a buoy marking the waters, the player is forced to consider they are bobbing back and forth to either side of it.
Let me give a concrete example of a moral dilemma. You have the trolley problem, with 5 strangers bound to one track and your fiance bound to the other. Does this problem change in difficulty if you have an alignment system? For like 5 of the 9 alignments, this isn't really a hard dilemma in theory. Chaotic evil or neutral obviously saves your fiance. Only four have a difficult choice because they have competing moral guidelines or competing self interest. But because both choices are evil, it probable that neither of those four alignments thank that either answer wrong or right. You can come up with Lawful Good answer for both based on duty. And yes, lawful systems generally define this as a hierarchy of personal duty. The answer they give will be different if your liege, child, or spouse is on one side or the other.
You know who has the biggest moral dilemma though? Suppose you have a lawful neutral character that knows his duty is to sacrifice his self-interest and save the many over the few. It's entirely possible that RP could cause him to pull a Javert here and forgo his duty and that would be interesting.
But my guess is that if you never made the player choose then this not a hard choice for a player and you'll never have a moral dilemma.
However that doesn't even touch on whether presenting a trolley problem deliberately in play is good DMing. If it comes up fine, but what is the motivation in deliberately creating "you can't win scenarios"?